On the correlations of masses and lifetimes of radionuclides and fundamental particles

Abstract

We show that for unstable fundamental particles and ß and a emitting nuclides the product of mass M (ergs) and lifetime T (seconds) can be expressed by the quantized form MT = ħ(2ⁿ/n) where n is an integer. The lifetime T is then expressible in the form T = (ħ/M)e^n/λ, where λ in the case of fundamental particles is a function of "n" only. In the case of β-emitters the mass M is that of the nucleon and in the case of a-emitters, the mass is equivalent to the binding energy of the nucleus. The log T vs n plots for the fundamental particles separate them out according to their flavor. The Heisenberg energy spread relation for decay can be written in the form ΔE = M(n/2ⁿ) shows the connection between the rest mass and lifetime through n. The ranges of n values indicate the strength of interaction during decay; n < 10 - strong, n = 10-30 - electromagnetic and "hidden strong" and n > 40 - weak. On this basis we set a lower limit of 6 × 10^-21 s for the weak decay of the top quark (mass ∼174 GeV). Some interesting mathematical properties of the functional form n/2ⁿ which is the backbone of the present analysis are discussed at the end of the paper.